Plato’s vision of Philosophy, Rational Rule, and the Good life

In our last meetup, we explored how Plato’s Republic is driven by a preoccupation with a crisis in Greek values. This crisis concerns the Meaning of terms like Dikaiosyne (Justice) and Arete (Virtue). The crisis emerged from an attempt to reconcile an archaic Homeric warrior ethic with the more refined ideals of parts of 4th-century Athens. In this meetup we attack the second half of the Republic.
Having established that True Arete and True Justice are conditions of a soul and a city whose parts are in order, and in which the rational part rules, Plato sets himself three interconnected main tasks for the rest of the Republic. Firstly, showing how rational rule can be established in the city and how it can be shown to be the best kind of rule, secondly, clarifying more precisely the relationship of rationality and goodness, and thirdly, solidifying the claim that the life of the Just man is better than the life of the unjust man.
Rational rule in the city, it turns out is the rule of the philosopher, and so Plato will suggest that in the ideal state it will be philosophers of the appropriate kind who rule. Thus, the nature of philosophy and the training of philosophers will need to be covered, but also the nature of rationality itself. For it will be found that rational rule is tied to knowledge of the good, and so the relationship of rationality to goodness must be explicated. This leads to some of the most famous and rhetorically brilliant passages in the history of Philosophy: The myth of the Cave, the allegory of the Ship of State, the Great Beast of the public and the keeper of the beast that is the unscrupulous sophist and politician, and likening the Good to the Light of the Sun.
But having achieved this vision of the interconnection of rationality and goodness, Plato returns to the project of showing that the life of the Just man and the Just City is the best kind of life. And since it is a fundamental assumption of the greeks that Human beings are made to live in city states, and a fundamental conclusion of Plato that the government of a city is analogous to the ordering of an individual soul, it follows that this will involve a comparative study of the different types of city state governments and of the type of man who organizes himself analogously to this form of government. This will be at once a study a study of social pathology and of the pathologies of the human soul, and when we have reviewed what is possible within this region, Plato sees we will see with great clarity, why Justice and rational rule are indeed the safest path to the good life for man.
Readings are linked here
https://drive.google.com/file/d/1CHYuRXZ6Fe2dmlPYhzHubXssj1MDXlqz/view?usp=sharing